Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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Warm Up Find the complement of each angle
measure. 1. 30 2. 42
60
48
Find the supplement of each angle measure.
4. 82
98
3. 150
30
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Problem of the Day Draw three points that are
not on the same line. Label them A, B, and C. How
many lines can you draw that are determined by
the points? Name the lines.
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Learn to identify parallel, perpendicular, and
skew lines, and angles formed by a transversal.
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Insert Lesson Title Here
Vocabulary
perpendicular lines parallel lines skew
lines vertical angles transversal
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When lines, segments, or rays intersect, they
form angles. If the angles formed by two
intersecting lines are equal to 90, the lines
are perpendicular lines.
Some lines in the same plane do not intersect at
all. These lines are parallel lines. Segments and
rays that are part of parallel lines are also
parallel.
Skew lines do not intersect, and yet they are
also not parallel. They lie in different planes.
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Additional Example 1A Identifying Parallel,
Perpendicular, and Skew Lines
Tell whether the lines appear parallel,
perpendicular, or skew.
A. UV and YV
The lines appear to intersect to form right
angles.
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Additional Example 1B Identifying Parallel,
Perpendicular, and Skew Lines
Tell whether the lines appear parallel,
perpendicular, or skew.
B. XU and WZ
The lines are in different planes and do not
intersect.
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Additional Example 1C Identifying Parallel,
Perpendicular, and Skew Lines
Tell whether the lines appear parallel,
perpendicular, or skew.
C. XY and WZ
The lines are in the same plane and do not
intersect.
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Try This Example 1A
Tell whether the lines appear parallel,
perpendicular, or skew.
A. WX and XU
The lines appear to intersect to form right
angles.
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Try This Example 1B
Tell whether the lines appear parallel,
perpendicular, or skew.
B. WX and UV
The lines are in different planes and do not
intersect.
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Try This Example 1C
Tell whether the lines appear parallel,
perpendicular, or skew.
C. WX and ZY
The lines are in the same plane and do not
intersect.
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Vertical angles are the opposite angles formed by
two intersecting lines. When two lines intersect,
two pairs of vertical angles are formed. Vertical
angles have the same measure, so they are
congruent.
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A transversal is a line that intersects two or
more lines. Eight angles are formed when a
transversal intersects two lines. When those two
lines are parallel, all of the acute angles
formed are congruent, and all of the obtuse
angles formed are congruent. These obtuse and
acute angles are supplementary.
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Reading Math
Angles with the same number of tick marks are
congruent. The tick marks are placed in the arcs
drawn inside the angles.
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Additional Example 2A Using Angle Relationships
to Find Angle Measures
Line n line p. Find the measure of the angle.
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A.
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Additional Example 2B Using Angle Relationships
to Find Angle Measures
Line n line p. Find the measure of the angle.
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B.
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Additional Example 2C Using Angle Relationships
to Find Angle Measures
Line n line p. Find the measure of the angle.
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C.
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Try This Example 2A
Line n line p. Find the measure of the angle.
45
4
5
6
2
3
135
7
n
p
3
A.
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Try This Example 2B
Line n line p. Find the measure of the angle.
45
4
5
6
2
3
135
7
n
p
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B.
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Try This Example 2C
Line n line p. Find the measure of the angle.
45
4
5
6
2
3
135
7
4
n
p
C.
In the figure, the acute and obtuse angles are
supplementary.
45
45
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Insert Lesson Title Here
Lesson Quiz
Tell whether the lines appear parallel,
perpendicular, or skew. 1. AB and CD 2. EF and
FH 3. AB and CG 4.
parallel
D
perpendicular
skew
How are railroad tracks and two parallel lines
alike, and how are they different?
Both are always the same distance apart, but
railroad tracks are not always straight.